The New Haven fire chief says the victims apparently consumed the synthetic marijuana known as K2, which may have also been laced with something else.
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Several victims were found passed out in and around a park across from Yale University.
A suspect has been arrested but it's not clear on what charges.
Most of the overdoses were on the New Haven Green, a popular, historic downtown park.
"Do not come down to the Green and purchase this K2," city Police Chief Anthony Campbell said. "It is taking people out very quickly, people having respiratory failure. Don't put your life in harm."
Paramedics and police officers were stationed at the park all day as more people fell ill. Some became unconscious and others vomited, authorities said. Emergency responders rushed to one victim as officials were giving a news conference nearby late Wednesday morning.
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"We literally had people running around the Green providing treatment," said Rick Fontana, the city's emergency operations director.
Police did not immediately release the name of the man who was arrested, saying they were waiting for victims to positively identify him.
New Haven first responders were called to a similar overdose outbreak on the Green on July 4, when more than a dozen people were sick from synthetic marijuana. The city also saw more than a dozen synthetic marijuana overdoses in late January. No deaths were reported in either outbreak.
Synthetic marijuana, which generally is plant material sprayed with chemicals that mimic the high from real marijuana, has been blamed for overdoses across the country.
Officials said the blood of Wednesday's victims was being tested to see what exactly they ingested. Fontana said a widely used anti-opioid-overdose drug given to some victims at the park did not seem to be effective, but the same drug did help some patients recover when given in higher doses at hospitals.
(The Associated Press contributed to this report.)